Theorem 5.10: Let the number of edges of G be m. Then G has a Hamilton circuit if m2(n 3n+6)/2, where n is the number of vertices of %o Proof: If any two vertices of G are adjacent, then G has a Hamilton circuit 192939···n1 o Suppose that u and v are any two vertices of G that are not adiacent o Let h be the graph produced by eliminating u and y from g Thus H has n-2 vertices and m-d(u-d(v) eages❖ Theorem 5.10: Let the number of edges of G be m. Then G has a Hamilton circuit if m≥(n2 - 3n+6)/2,where n is the number of vertices of G. ❖ Proof: If any two vertices of G are adjacent ,then G has a Hamilton circuit v1 ,v2 ,v3 ,…vn ,v1 . ❖ Suppose that u and v are any two vertices of G that are not adjacent. ❖ Let H be the graph produced by eliminating u and v from G. ❖ Thus H has n-2 vertices and m-d(u)-d(v) edges